You happen to choose the only sniper rifle that you cannot change the barrel on. The VKS has a built in silencer so there is no option to replace the barrel. Choose any of the other 3.. my favorite is the USR (havent tried the others but i havent had a need to try the others )

Here we’ll go over how you can unlock the Ghillie Suit for multiplayer.

Snipers wear a Ghillie Suit’s camouflage clothing to blend into their surroundings, as an optimal way to hide themselves from enemies and take out their targets in stealth. The outfit works especially well in high grass.

Take these steps to successfully unlock the Ghillie Suit:

• Step #1: It turns out the only suit-unlocking challenges you can work on are those listed in the Operations menu. So at any given time you only have the choice to go and unlock suits (or any other gear like patches) given by completing 10 random challenges in each of the 5 categories shown in the Operations menu. New challenges arrive every two weeks, which is why you see the countdown timer in the bottom-right corner of that menu, that’s how much time you have left to complete your current challenges.

• Step #2: Next, be sure to set the 5 challenges for the Ghillie Suit (and any patches you’re after) that you want are set on the front page; to do this go to the un-completed challenges in the menu and hit the button/key to make it active (X on Xbox / Square on PlayStation).

By adding them to the top 5 challenges you’re after, your progress for those 5 challenges there won’t get lost when you reset the Operations challenges by spending 1 Squad Point to get 50 new challenges to choose from! The reasoning behind buying new challenges over and over (instead of waiting two weeks for it to happen automatically) is to find the challenges that allow you to unlock the Ghillie Suit (and any new gear that you’re after), since not all are available at the same time. Step 3 will clarify which challenges you’re look for.

• Step #3: Now on to completing the following “Master” challenges to unlock the Ghillie Suit:

A) Under “Weapon Operations” look for the “Chrome Barrel Master I” & “Variable Zoom Master I” challenges. These require you to “Get 100 kills with the Chrome Barrel attachment” & “Get 100 kills with the Variable Zoom Sight”, respectively. You must complete these type of one-shot kills with the Chrome Line sniper rifle attachment. Then spend 1 Squad Point to unlock all-new challenges. When the game asks “Notice: Confirm New Operations Purchase?” choose “Yes”, which will make your next two challenges appear!

C) Under “Weapon Operations” look for the “Chrome Barrel Master III” newly upgraded challenge. It requires you to “Get 500 kills with the Chrome Barrel attachment”. Complete it to unlock the Ghillie Suit!

Note: Once the final challenge is done, the unlocked suits will stay yours forever, since the game saves your unlocking progress once a challenge gets completed.

This is a great answer but I agree with celehti that the question is still not answered because NONE of the sniper rifles in PS4 version of Ghosts has a chrome barrel attachment. So how come all these guys are running around in ghillie suits? What am I missing here? Would somebody please answer this question?